Work

Operator-Based Approach for the Construction of Solutions to (CD(1/n))k-Type Fractional-Order Differential Equations

Year: 2025

Type: article

Abstract: A novel methodology for solving Caputo D(1/n)Ck-type fractional differential equations (FDEs), where the fractional differentiation order is k/n, is proposed. This approach uniquely utilizes fractional power series expansions to transform the original FDE into a higher-order FDE of type D(1/n)Ckn. Significantly, this perfect FDE is then reduced to a k-th-order ordinary differential equation (ODE) of a special form, thereby allowing the problem to be addressed using established ODE techniques rather than direct fractional calculus methods. The effectiveness and applicability of this framework are demonstrated by its application to the fractional Riccati-type differential equation.

Source: Mathematics

DOI: 10.3390/math13071169

Authors: Inga Telksniene, Zenonas Navickas, Romas Marcinkevičius, Tadas Telksnys, Raimondas Čiegis, Minvydas Ragulskis

Institutions: Vilnius Gediminas Technical University, Kaunas University of Technology

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Lietuvos Mokslo Taryba